Can someone who never snored start snoring?

Yes, it is definitely possible for this to happen.
This could happen if :

The person has gained a lot of weight (one of the factors to battle snoring is often a recommendation by the doctor to lose the excess weight)

There is some kind of an obstruction in the tongue or in the breathing passageways

What you can do for a start is try to lie down in a different position. For example if the person snores when laying on his or her back then try either of the sides. Different positions result in different pressures and it may be possible to have clear airways in one position and not another.

If you have addressed the weight and tried different positions and the problems still remains then you need to go see a doctor to properly check what the issue is.